Atkin-Lehner |
3- 23+ 101- |
Signs for the Atkin-Lehner involutions |
Class |
6969b |
Isogeny class |
Conductor |
6969 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
7392 |
Modular degree for the optimal curve |
Δ |
-1117040103 = -1 · 32 · 233 · 1012 |
Discriminant |
Eigenvalues |
1 3- -4 4 6 -2 -8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,152,-1423] |
[a1,a2,a3,a4,a6] |
Generators |
[1207:41336:1] |
Generators of the group modulo torsion |
j |
392062442759/1117040103 |
j-invariant |
L |
5.2046546569215 |
L(r)(E,1)/r! |
Ω |
0.79431992300251 |
Real period |
R |
6.5523405698399 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
111504n1 20907a1 |
Quadratic twists by: -4 -3 |